Exam 19: Dc Circuits

A series circuit contains a 20- $\Omega$ resistor, a 200- $\mathrm { mH }$ inductor, a $10 - \mu \mathrm { F }$ capacitor, and an ac power source. At what frequency should the power source drive the circuit in order to have maximum power transferred from the driving source?

At $1.0 \mathrm { kHz }$ , the phase angle of an $R L C$ series circuit with a capacitive reactance of $40 \Omega$ , a resistance of $100 \Omega$ , and a certain inductor is $40 ^ { \circ }$ . What is the inductance in this circuit?

A galvanometer has an internal resistance of $100 \Omega$ and deflects full-scale at $2.00 \mathrm {~mA}$ . What size resistor should be added to it to convert it to a milliammeter capable of reading up to $4.00 \mathrm {~mA}$ ?

If $V = 20 \mathrm {~V}$ and the battery is ideal, what is the current through $R _ { 3 }$ in the figure?

A conducting rod of length $\ell = 25 \mathrm {~cm}$ is placed on a $U$ -shaped metal wire that is connected to a lightbulb having a resistance of $8.0 \Omega$ , as shown in the figure. The wire and the rod are in the plane of the page. A constant uniform magnetic field of strength $0.40 \mathrm {~T}$ is applied perpendicular to and into the paper. An applied external force pulls the rod to the right with a constant speed of $6.0 \mathrm {~m} / \mathrm { s }$ . What is the magnitude of the emf induced in the rod?

In the circuit shown in the figure, the $60 - \mathrm { Hz }$ ac source has a voltage amplitude of $120 \mathrm {~V}$ , the capacitive reactance is $800 \Omega$ , the inductive reactance is $300 \Omega$ , and the resistance is $560 \Omega$ . What is the phase angle?

What resistance must be connected in parallel with a $633 - \Omega$ resistor to produce an equivalent resistance of $205 \Omega$ ?

A 100-W light bulb is powered by 120 V ac 60.0-Hz household connection. Determine the rms current and the current amplitude.

A single-turn loop of wire, having a resistance of $8.00 \Omega$ and a cross-sectional area $200 \mathrm {~cm} ^ { 2 }$ , is perpendicular to a uniform magnetic field that increases steadily from $0.200 \mathrm {~T}$ to $2.800 \mathrm {~T}$ in $2.20$ seconds. What is the magnitude of the induced current in the loop?

A conducting rod whose length is $\ell = 27.0 \mathrm {~cm}$ is placed on frictionless $U$ -shaped metal rails that is connected to a lightbulb having a resistance of $5.00 \Omega$ as shown in the figure. The rails and the rod are in the plane of the page. A constant uniform magnetic field of strength $1.20 \mathrm {~T}$ is applied perpendicular to and out of the paper. An external applied force moves the rod to the right with a constant speed. At what speed should the rod be pulled so that the lightbulb will consume energy at a rate of $1.10 \mathrm {~W}$ ?

A 200- $\Omega$ resistor, a $40 - \mathrm { mH }$ inductor, and a $2.0 - \mu \mathrm { F }$ capacitor are connected in series with a $120 - \mathrm { V }$ rms source at $1.0 \mathrm { kH }$ . What is the phase angle of this circuit?

An ideal transformer has 60 turns on its primary coil and 300 turns on its secondary coil. If $120 \mathrm {~V}$ at $2.0 \mathrm {~A}$ is applied to the primary, (a) what voltage is present in the secondary? (b) what current is present in the secondary?

A $2.00$ -m long metal wire is formed into a square and placed in the horizontal $x y$ -plane. A uniform magnetic field is oriented at $30 ^ { \circ }$ above the horizontal with a strength of $0.344 \mathrm {~T}$ . What is the magnetic flux through the square due to this field?

The capacitive reactance of a 44- $\mu \mathrm { F }$ capacitor in an ac circuit is $6.0 \times 10 ^ { 2 } \Omega$ . What is the frequency of the applied signal?

Consider a series circuit in which the capacitive reactance equals the inductive reactance. What is the phase angle between current and voltage for this circuit?

As shown in the figure, a C-shaped conductor is in a uniform magnetic field $B$ out of the page, and this field is increasing. What is the polarity of the induced emf in terminals $X$ and $Y$ ?

For a series ac circuit consisting of a resistance of $13.0 \mathrm { k } \Omega$ , a capacitance of $7.0 \mu \mathrm { F }$ , and an inductance of $35.0 \mathrm { H }$ , what frequency is needed to minimize the impedance if the voltage amplitude is $110 \mathrm {~V}$ ?

An ideal 100- $\mathrm { V }$ dc battery is applied across a series combination of four resistors having resistances of $20 \Omega , 40 \Omega , 60 \Omega$ , and $80 \Omega$ . What is the potential difference across the $40 - \Omega$ resistor?

A $5.0 - \mu \mathrm { F }$ , a $14 - \mu \mathrm { F }$ , and a $21 - \mu \mathrm { F }$ capacitor are connected in parallel. How much capacitance would a single capacitor need to have to replace the three capacitors?

The phase angle in a series $R L$ circuit at $1.0 \mathrm { kHz }$ with a $0.20 - \mathrm { k } \Omega$ resistor and a certain inductor is $40 ^ { \circ }$ . What is the inductance in this circuit?